What is the ruling on sleeping with the light on in the bedroom, and does this ruling differ between men and women?

There is nothing in the Shariah that specifies the presence of light in the bedroom for men or women. As for the Sunnah (definition), it guided to extinguishing lamps when sleeping, fearing that the house might burn down due to a mouse dragging the wick, as stated in Sahihayn, from Jabir ibn Abdullah, may Allah be pleased with them both: "Extinguish the lamps when sleeping, for the wicked little creature (mouse) might drag the wick and burn the occupants of the house." And in Sunan Abi Dawud, from Ibn Abbas, the Messenger of Allah, peace and blessings be upon him, said: "When you sleep, extinguish your lamps, for the devil guides such as these to this, and they burn you."

As for electric lights, this command does not apply to them, as the cause of the house burning down is absent in their case, as stated in Al-Nawawi's commentary on Muslim, where he said: "When the cause is removed, the prohibition is lifted."